In order to study interactions between DNA molecules and other components, such as proteins, it is known to submit the DNA molecules to stretching forces and to measure the elastic properties (i.e. relative extension versus force characteristics) of the molecules.
Document US 2003/0027187 discloses for instance an apparatus for testing a DNA molecule wherein the molecule is anchored at one end to an anchoring surface and at the other end to a paramagnetic bead. The apparatus comprises magnets for applying a force to the bead so as to control the stretching and torsion of the molecule. The apparatus also comprises a light source, a microscope and a camera for generating an image of the bead, as well as a computer for analyzing the image generated.
Analysis of the image of the bead allows determining in real time the position of the bead in three dimensions (x, y, z), and thus the extension of the molecule and the applied stretching force.
The x, y coordinates of the bead may be determined by using the symmetry of the bead and determining its center by auto-convolution. Indeed, this function presents a maximum positive value which position is shifted by (2δx, 2δy) where δx(δy) is the shift of the bead image along x(y) from the original image center. Auto-convolution may be computed rapidly using a FFT algorithm and the maximum position may be obtained by locally fitting a second order polynomial.
The z coordinate of the bead (i.e. coordinate of the bead along the magnification axis of the microscope) may be determined by comparing the diffraction pattern of the bead to a set of reference diffraction patterns previously acquired during a calibration phase.
Indeed, interferences between light radiations emitted by the light source and light radiations diffused by the bead generate diffraction rings in the image recorded by the camera. The size of the diffraction rings varies with the distance of the bead relative to the focal plane of the microscope.
Calibration of the apparatus consists in recording several images of the bead by varying focusing of the microscope while keeping the bead in a fixed position relative to the anchoring surface. This calibration phase allows generation of different reference images of the bead corresponding to different distances between the bead and the focus plane.
Once the calibration phase has been completed, comparison of the current image of the bead with the reference images, allows measurement of the position of the bead with a precision of few nanometers. For instance, the method allows following positions of a few dozen of beads, with a precision of about 3 nanometers between two video images. In applications wherein the apparatus is used for measuring the length of the DNA molecule, this allows localizing a sequence component of the DNA molecule to within few nucleobases.
However, the calibration phase is time consuming, requires large computing resources and must be carried out for each bead separately.
Moreover, the proposed method requires the use of a large number of pixels on the camera used to image one bead, especially if one wishes to test long DNA molecules because of the increasing of the size of the image of the object. This may limit the number of beads one is able to analyze (for instance 1000 beads for a 4 megapixels camera).
Therefore, the proposed method may not be extended for simultaneously measuring positions of a large number of beads, such as thousands of beads for instance.
In addition, in order to vary focusing of the microscope, the calibration phase requires the use of a high precision nano-positioning stage, including piezoelectric actuators, for moving the anchoring surface relative to the microscope in a precise and repeatable way.